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Systemic Risk and Sentiment
May 24 2012
X JORNADA DE RIESGOS FINANCIEROS RISKLAB-MADRID
Giovanni Barone-Adesi
Swiss Finance Institute
and University of Lugano
Loriano Mancini
Swiss Finance Institute
and EPFL
Hersh Shefrin
Leavey School of Business
Santa Clara University
Abstract
•
The foundations of risk management are rooted in the efficient market hypothesis.
If prices are subject to behavioral biases, regulators charged with monitoring
systemic risk need to focus on sentiment as well as narrowly defined measures of
systemic risk.
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This paper describes techniques for jointly monitoring the co-evolution of
sentiment and systemic risk. To measure systemic risk, we use Marginal Expected
Shortfall. To measure sentiment, we apply a behavioral extension of traditional
pricing kernel theory, which we supplement with external proxies.
•
We illustrate the technique by analyzing the dynamics of sentiment before, during,
and after the global financial crisis which erupted in September 2008.Using stock
and options data for the S&P 500 during the period 2002–2009, our analysis
documents the statistical relationship between sentiment and systemic risk. The
misperception of risk by the representative investor causes a reversal of the
perceived risk-expected return trade-off.
Systemic Risk and Sentiment
• The report of the Financial Crisis Inquiry Commission (FCIC,
2011) emphasizes the importance of systemic risk and
sentiment. These two concepts, and the relationship
between them, are important for regulatory bodies.
• The FCIC describes systemic risk as “a precipitous drop in
asset prices, resulting in collateral calls and reduced
liquidity.” In its report, the FCIC criticized regulators for
viewing “the institutions they oversaw as safe and sound
even in the face of mounting troubles,” and concluded that
“dramatic failures of corporate governance and risk
management at many systemically important financial
institutions were a key cause of this crisis.
• We will explore the evolution of systemic risk, leverage and
sentiment as the crisis unfolded.
Measuring Systemic Risk
• There is no consensus on the measure or the prediction of
systemic risk. It is likely to be non-linear in nature, that
makes prediction problematic. We use Marginal Expected
Shortfall, (MES), defined for a firm as the expected equity
loss per dollar conditional on the occurrence of a systemic
event.
• An example of a systemic event is a decline in the value of
the market portfolio on a given day by 2% or more. Values
for MES are reported at New York University’s Volatility Lab
website.
• MES is computed as a function of volatility, correlation with
the market return, and the tail expectation of the
distribution of standardized innovations.
Measuring Sentiment
• Our main contribution is the introduction of a measure of
sentiment based on a behavioral analysis of market returns.
• Statistically, building on Shefrin’s work, we take point by
point the log-difference between the pricing kernel
computed as in BEM and the pricing kernel under CRRA.
• We validate our measure of sentiment by comparing it to
traditional measures of sentiment from investor surveys.
• The practical advantage of our measure is that it can be
computed instantly from market data, rather than relying
on monthly surveys.
Optimism and Overconfidence
• We focus on the first two moments of
sentiment. Optimism relates to expected
return, overconfidence to understatement of
risk.
• We also relate optimism to leverage and (lack
of) to MES and perceived crash probability.
Three Probability Measures
• Financial economists use commonly the
objective and the pricing probability measure.
• We introduce a third measure for the
representative investor. That is computed by
projecting a semiparametric price kernel on a
CRRA price kernel.
• Our representative investor’s price kernel is
validated by comparison to survey data.
Sentiment: from survey (CP) and from
market return (CPF1)
.20
.15
.10
.05
60
.00
50
-.05
40
30
20
10
2002
2003
2004
CP
OVERCON
2005
2006
CPF1
LEFTREP
2007
2008
2009
OPTIMISM
Risk premium under the objective or
the represntative investor’s measure
• The objective risk premium rose sharply from a
low of about 2.4% in 2002 to about 4% several
months later, after which it followed a downward
path, with considerable volatility, dipping close to
zero in 2007. It then rose sharply over the next
few months, to about 6.5%, before falling to
about 5% at the end of the sample period.
• The representative investor’s risk premium
followed a different pattern, fluctuating between
2% and 4% for most of the sample period.
Figure 3
Risk premium
.07
.06
.05
.04
.03
.02
.01
.00
2002
2003
2004
2005
RISKPREMOBJ
2006
2007
2008
RISKPREMREP
2009
Risk and expected return under the
objective measure
• With respect to our sample, risk aversion generally
declined during 2002 from about 1.3 to 0.3, and then
rose in a wave pattern through late 2007, first
increasing through 2005 above 3.0, falling through mid2006 to just under 1.0,rising again until 2007, and then
falling dramatically with volatility, reaching zero in the
aftermath of the Lehman Brothers bankruptcy. Risk
aversion then rose through the last part of the sample
period.
• Notably, risk aversion was at its lowest during the
down markets at the beginning and end of the sample
periods and highest in the up market during the middle
period.
Risk/Return
• The trade-off between risk and EXPECTED
return is positive under the objective
measure, negative under the representative
investor’s measure.
• The trade-off between risk and return is
positive under both measures. After the crash,
expected return and risk are positively related,
possibly because of sentiment changes.
1.075
1.07
6
1.070
1.065
EXPREPINV
EXPOBJ
1.060
1.06
1.055
1.050
1.05
1.04
1.045
1.03
1.040
1.035
1.02
10
20
30
40
50
60
70
80
90
100
10
20
30
40
50
VIX
60
70
80
90
100
VIX
1.075
1.07
1.070
1.06
1.065
EXPREPINV
EXPOBJ
1.060
1.055
1.050
1.05
1.04
1.045
1.03
1.040
1.035
1.02
.12
.16
.20
.24
.28
.32
STDOBJ
.36
.40
.44
.05
.10
.15
.20
STDREPINV
.25
.30
.35
The Solution of the Puzzle: optimism
and overconfidence
• What drives the negative slope is optimism and
overconfidence. They are positively correlated. If
they both go up (or down) together by enough,
then when the representative investor's expected
return goes up because of increased optimism,
his return standard deviation simultaneously
tends to go down because of increased
overconfidence. In our sample, for monthly
observations, the correlation between optimism
and overconfidence is 0.65. For weekly
observations, the correlation is 0.5.
Crash Confidence 2002-2009
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At the beginning of the sample period, the crash confidence index CP was low,
below 30. During 2002, it rose to about 40 and then fell sharply to about 21.
Between 2003 and late 2007, the crash confidence index trended up, peaking just
Below 60. During the decline, crash confidence fell to the mid 30s, where it
remained until the Lehman Brothers bankruptcy. After the bankruptcy, crash
confidence fell sharply, bottoming below 20. As with RMSE and MAE, it too
dropped sharply in 2007 and the last portion 2008, as earnings declined sharply.
In this respect, CP provides external corroboration for the evolution of optimism
and overconfidence.
There is reason to suggest that CP serves as an indicator of systemic risk.
High values of CP suggest that the majority of institutional investors attached
not just low probability, but insufficient probability, to outlying events. Keep in
mind that the Yale/Shiller indexes are indicators of the proportion of those holding
particular views. Other indexes are also informative. The value confidence
index, both for institutional investors and individual investors rose during 2008,
suggesting that investors increasingly viewed the market decline during this period
to have been an overreaction. A similar statement applies to the one-year
confidence indexes.
MES
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We link our results to individual companies using MES. MES is “the expected
equity loss per dollar invested in a particular company if the overall market
declines by a certain amount.” That is 2% in our study. We use MES to follow
individual firms through the 2008 crash.
MES measures expected equity loss for a financial firm if the market loss
exceeds2% on a daily basis. Bear Stearns, in April 2008, had an MES of 12.4%
(Vlab, NYU). Lehman Brothers, which declared bankruptcy in September, had
an MES of 8.75%. AIG’s MES stood at 6.21%. Merrill Lynch, the dominant
underwriter of CDOs, which needed to be acquired by Bank of America at
year-end, was close behind at 8.15%.
In March 2007, MES values had been considerably lower. Bear Stearns’s MES
was at 4.5%, as was the MES of Lehman. By the end of September when
Lehman declared bankruptcy, AIG’s MES had soared to 25.8%. Citigroup,
Merrill Lynch, Morgan Stanley, and even JP Morgan Chase all had MES values
above 8%. Goldman Sachs stood out as an exception, with an MES of 6.5%. By
this time, the market had turned from being optimistic to being pessimistic (by
over 1%). Notably, overconfidence soared to almost 8%, as investors seriously
underestimated future volatility.
MES and Leverage
• The relationship between systemic risk and sentiment is complex. If
one asks how sensitive was MES to changes in sentiment, the
answer is that it was highly firm-dependent. For Bank of America,
the correlation between MES and optimism was 84%. For Fannie
Mae and Freddie Mac, MES was 72% and 77% respectively. For
Citigroup, it was 71%. For AIG, it was 48%. For Bear Stearns, it was
41%. Notably, for Goldman Sachs, it was 36%. Correlations of MES
with overconfidence are much lower than for optimism, and also
vary in sign.
• If one asks about the correlation of leverage with optimism, the
answer is that these tended to be large and negative, in the range
of 70% and below. Goldman Sachs was an exception, at 35%.
However, the correlations of leverage with overconfidence were
closer to zero, and mixed in sign.
Conclusion
We propose a method to estimate the representative
investor’s biases and their impact on systemic risk from
market data.
We find evidence of the changing optimism and
confidence through the last decade. They play an
important role in explaining the trade-off between risk
and expected return.
Our market-based variables correlate well with results of
surveys of investor sentiment.
A long period of low perceived risk is associated to
optimism and increasing leverage, showing a build-up in
systemic risk.